We recall that the inclusions \(A_1 \subset A_p \subset A_q\)  hold for \(1 \le p \le q.\) 
Also, it is immediate that \(w\in A_p\) , for \(1<p<\infty \) , if and only if \(w^{1-p^{\prime }}\in A_{p^{\prime }},\) 
and then \([w^{1-p^{\prime }}]_{A_{p^{\prime }}} = [w]_{A_p}^{1/(p-1)}.\) 
Here \(p^{\prime }=\frac{p}{p-1}\)  is the conjugate exponent of \(1<p<\infty .\) 
See [1]} for an introduction to the theory of Muckenhoupt weights.
